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Small Area Income & Poverty EstimatesModel-based Estimates for States, Counties, & School Districts |
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The 1995 state and county estimates were released in February of 1999. The methodology used to produce these estimates was very similar to that used in the production of the 1993 state and county estimates. For an overview of the changes in methodology between the production of the 1995 and 1993 state and county estimates, please see Estimation Procedure Changes.
Here are some points to consider about the 1995 estimates of poverty for counties:
Using counties in the CPS sample. Our use of the CPS implicitly assumes that the counties in the survey sample are representative of those not selected, but this need not be the case. The CPS sample is designed to represent the population and only incidentally represents counties. The characteristics of some counties guarantee that they are included, e.g., most counties in large metropolitan areas and counties with large populations. More generally, while all counties have a nonzero probability of being included in the sample, some have higher probabilities than others. Further, the probability of selection of a county may be related to its income and poverty level. On the other hand, comparison of regression equations based on 1990 census data for counties in the CPS sample and equations based on all counties indicate remarkably similar results, providing some assurance that the CPS counties are largely representative of all counties.
The survey weights used in estimation at the national level are not appropriate for county-level estimates. The CPS sample design selects some primary sampling units (usually a county or group of counties) to represent a set of counties in the same stratum. The sum of the weights for sample households from such a county estimates the total population of the entire set of counties it represents. Because we want each county in the CPS sample to stand for itself, we have adjusted the weights to make each county self-representing.
Estimation of the model equation. CPS sampling variances are not constant over all counties. We avoid giving observations with larger variances (a great deal of uncertainty) the same influence on the regression as observations with smaller variances (less uncertainty) by, in effect, weighting each observation by the inverse of its uncertainty. Representing this uncertainty requires recognizing that it arises from two sources:
To estimate the lack-of-fit component, we estimate our model using the 1990 census data and assume that the lack-of-fit component of residual variance is the same when the same model is fit to the CPS and to the census. Since we have separate estimates of sampling variance for each observation in the 1990 census, we use them to estimate the unknown lack-of-fit component with a maximum likelihood procedure. (See "Appendix C: Accuracy of the Data" in 1990 Census, STF3 documentation.)
Next we fit a regression equation to the CPS data. We assume the sampling variance of the log of the number of poor is inversely proportional to the sample size (in households) and the lack-of-fit variance is the same as that estimated in the census regression. We estimate the CPS regression parameters and the two components of CPS variance with a maximum likelihood procedure.
Combining model and direct survey estimates. The final estimates are weighted averages of the model predictions and the direct CPS estimates, where they exist. The two weights for each county add to 1.0, and we compute the weight on the model prediction as the sampling variance divided by the total variance (sampling plus lack-of-fit) of the direct estimate. With this technique, the larger the sampling variance of the direct estimate, the smaller its contribution and the larger the contribution from the prediction model. These weights are commonly referred to as "shrinkage weights," and the final estimates as "shrinkage" or "Empirical Bayes" estimates. For counties not in the CPS sample, the weight on the model's predictions is one and the weight on the direct survey estimate is zero.
Controlling to State Estimates. Completing the shrinkage estimates does not produce the final county estimates of the number of poor. The last steps in the production process are transforming the county estimates from the log scale to estimates of numbers and controlling them to the independently derived state estimates. We make a simple ratio adjustment to the county-level estimates to ensure that they add to the state totals. We control model-based estimates at the state level to the national level direct estimates derived from the March 1996 CPS. We adjust the estimated standard errors of the county estimates to reflect this additional level of control.
We do not control estimates of county median household income to the state medians because the estimation model does not produce the entire household income distribution, which would be required to do so.
Standard Errors and Confidence Intervals. One goal of our small area estimation work is providing estimates of the uncertainty surrounding the estimates of the numbers of poor. The census and model-based estimates shown in the tables are accompanied by their 90-percent confidence intervals. These intervals were constructed from estimated standard errors.
For the model-based estimates, the standard error depends mainly on the uncertainty about the model and the CPS sampling variance. While the variance of the shrinkage weights could also be a significant component of uncertainty about our estimates (if sizeable and ignored we would be underestimating the standard errors), our research indicates that its contribution is negligible.
For the census, we derive the standard errors from a set of generalized variance functions that reflect the nature of the census sample design for the long form questionnaire. (For further information, see Quantifying Uncertainty in the Estimates.)
The Model for Total Number of Poor PeopleThe model is multiplicative; that is, we model the number of poor as the product of a series of predictors that are numbers (not rates), and we model the unknown errors. To estimate the coefficients in the model, we take logarithms of the dependent and all independent variables. Our choice of a multiplicative model is motivated in part by the fact that the distribution of the number of poor has a huge range -- from zero in some counties to more than a million in the largest county (with a mean of 10,000), based on the 1990 census -- and the distribution is highly skewed. Taking the logarithm of all variables makes their distributions more centered and symmetrical and has the effect of diminishing the otherwise inordinate influence of large counties on the coefficient estimates. Another advantage of a multiplicative model is that it makes it plausible to maintain that the (unobserved) errors for every county, no matter how large or small, are drawn from the same distribution.
The predictor variables in the regression model used to estimate the total number of poor people by county for income year 1995 are:
For further information on these variables see Information about Data Inputs.
The dependent variable is the log of the total number of poor in each county as measured by the three-year average of values from the March CPSs for 1995, 1996 and 1997. We combine the regression predictions, in the log scale, with the logs of the direct CPS sample estimates, and then transform the results into estimates of the numbers of poor. Finally, we control the estimates to the independent estimates of state totals.
The Model for the Number of Related Children Ages 5 to 17 in Families in Poverty
The estimation model for related children age 5 to 17 in poverty parallels that for all people in poverty in structure. There are five predictor variables:
For further information on these variables see Information about Data Inputs.
The dependent variable is the log of the number of poor related children age 5 to 17 in each county as measured by the three-year weighted average of the March CPSs for 1995, 1996 and 1997. We combine the regression predictions, in the log scale, with the logs of the direct CPS sample estimates, and then transform the results into estimates of the numbers of poor. Finally, we control the estimates to the independent estimates of state totals.
The Model for the Number of Poor People Under Age 18
The estimation model for poor people under age 18 in poverty is quite similar. There are five predictor variables:
For further information on these variables see Information about Data Inputs.
The dependent variable is the log of the number of poor people under age 18 in each county as measured by the three-year weighted average of the March CPSs for 1995, 1996 and 1997. We combine the regression predictions, in the log scale, with the logs of the direct CPS sample estimates, and then transform the results into estimates of the numbers of poor. Finally, we control the estimates to the independent estimates of state totals.
The Model for Median Household Income
The predictor variables in the regression model we use to generate the estimates for median 1995 household income by county are:
For further information on these variables see Information about Data Inputs.
The dependent variable is the county median household income as measured by the three-year average of the March CPSs for 1995, 1996 and 1997 (income for years 1994, 1995 and 1996, respectively). We adjusted the March 1995 and 1997 CPSs to express incomes in 1995 dollars before we computed the median incomes.